SOLVING OVERSAMPLED DATA PROBLEMS BY MAXIMUM ENTROPY.

A numerical algorithm for the solution of the Classic Maximum Entropy problem is presented, for use when the data are considerably oversampled, so that the amount of independent information they contain is very much less than the actual number of data points. Examples of problems for which this algorithm is particularly appropriate are dynamic light scattering, solution scattering and fibre diffraction. The application of a general purpose entropy maximisation program is then comparatively inefficient. In the new algorithm the independent variables are in the singular space of the transform between map (or image or spectrum) and data, and much fewer in number than either the data or the reconstruction. This reduction in the dimension allows a direct evaluation of the posterior probability of the solution, and thus enables the ‘Classic Maxent’ problem to be solved completely.

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